Model application and result verification
1) Harmonic constant verification
Table 2.1 shows the comparison between the harmonic constant of constituent М2 simulated by the model and the harmonic constant observed at the tidal stations in the CircumBohai Sea Region and Yellow Sea. The average amplitude error simulated at the 19 tidal stations is only 4.5 cm, the average error of the tidal epoch is only 4.2°. The harmonic constant obtained after stabilized calculation is consistent with the observation results. The causes of the difference may be the following: (1) the location difference between the grid points and the tidal stations, for the model’s horizontal grid spacing is thousands of meters, and such a grid still has poor coastline resolution; (2) changes in the boundary and errors in topography and water depth, which are especially obvious at Yellow River Estuary and Laizhou Bay; (3) the harmonic constant precision of the constituents at the boundary.
Figures 2.21 through 2.24 show the cotidal hours of the tidal constituents М2. S‘2. A’i and О i of the simulated Bohai Sea and Yellow Sea, which match the distribution characteristics of the charts of the Bohai Sea, the Yellow Sea and the East China Sea.
TABLE 2.1: Comparison between the harmonic constant of М2 observed at the tidal stations
Measuring point 
Amplitude (cm) 
Phase (°) 
Error (observed value calculated value) 
Error (observed value calculated value) 

Dengsha River 
7 
8 
Lvshun 
10 
0 
Yangtouwa 
1 
8 
Beihuangcheng 
10 
1 
Caofeidian 
2 
0 
Qiansuowai 
7 
0 
Huangdi 
0 
10 
Changshansi 
2 
5 
Y ingkou 
7 
5 
Bayuquan 
0 
0 
Changxing Island 
4 
6 
Hulutao 
10 
8 
Y ingchengziwan 
9 
9 
Flat form 28 
8 
0 
Yantai 
2 
6 
Longkou 
1 
7 
Tanggu 
0 
0 
Hulu Island 
4 
0 
Dalian 
3 
6 
Average error 
4.5 
4.2 
FIGURE 2.21: The calculated isoamplitude line (cm) and cotidal line (°) of the constituent М2 in Bohai Sea and Yellow Sea (the dotted line is the isoamplitude line (cm); the solid line is the cotidal line (°))
FIGURE 2.22: The calculated isoamplitude line (cm) and cotidal line (°) of the constituent S2 in Bohai Sea and Yellow Sea (the dotted line is the isoamplitude line (cm); the solid line is the cotidal line (°))
FIGURE 2.23: The calculated isoamplitude line (cm) and cotidal line (°) of the constituent Кj in Bohai Sea and Yellow Sea (the dotted line is the isoamplitude line (cm); the solid line is the cotidal line (°))
FIGURE 2.24: The calculated isoamplitude line (cm) and cotidal line (°) of the constituent О in Bohai Sea and Yellow Sea (the dotted line is the isoamplitude line (cm); the solid line is the cotidal line (°))
Since there are many islands in the Bohai Strait, its current field structure is very complicated [49, 50]. When the tidal current is introduced into the Bohai Sea from the open sea, the islands distributed in the Bohai Straits divide the straits into six main waterways, so that the current rate will inevitably increase due to the sudden narrowing of the waterways. Among all the waterways, Laotieshan Waterway, located in the northernmost part, is the deepest and has the largest current velocity. At low tide, the residual current of a small amount of ebb tide still has a relatively large current rate when it passes through the narrow waterways between islands and presents righthand helic ity, and the tide will turn in the next moment. Due to the characteristics of free refinement of the unstructured grid in the FVCOM model, the grid refinement in the Bohai Strait can finely distinguish many islands in the strait and more accurately simulate the current field in the Bohai Strait (as shown in Figures 2.25 through 2.27).
FIGURE 2.25: Current field at low tide in Bohai Strait
FIGURE 2.26: Current field in the middle of flood tide in Bohai Strait
FIGURE 2.27: Current field in the middle of ebb tide in Bohai Strait
Oneyear tidebound waterlevel and marinecurrent observations were made at Changxing Island Observatory (39°30.433’N, 121°16.320'E) from March 15, 2008 to March 20, 2009. The tide and tidal current were harmonized with the observed data, and the harmonized results were then compared with the numerical simulation results, as shown in Table 2.2. The comparison indicates that the average error of the tidal epoch is 9.3°, and the average error of tidal amplitude is 5.7 cm; the average error of tidal epoch is 9.4° and the average error of tidal amplitude is 2.4 cm. The numerical simulation results are in good agreement with the observed results.
TABLE 2.2: Comparison of harmonic constant of tidal current and tide level observed at Changxing Island Observatory
Element 
Tidal constituent 
Harmonic constant 

North component (observed) 
North component (simulated) 
Error 

Delay angle (°) 
Amplitude (cm) 
Delay angle (°) 
Amplitude (cm) 
Delay angle (°) 
Amplitude (cm) 

Tidal current 
Oi 
306 
8.3 
293.96 
6.57 
12.04 
1.73 
hi 
359 
12.8 
345.63 
10.49 
13.37 
2.31 

М2 
19 
58.1 
4.07 
46.31 
14.93 
11.79 

•Ь'2 
80 
17.3 
75.04 
10.41 
4.96 
6.89 

Tide bound water level 
28.4 
22.3 
23 
18.91 
5.4 
3.39 

Fi 
71.5 
27.9 
62.57 
22.81 
8.93 
5.09 

М2 
35 
42.8 
36.28 
43.65 
1.28 
0.85 

84.9 
14.1 
56.27 
12.3 
28.63 
1.8 
2) Verification of tidal current
A total of 13 comparisons of the data at point A (120°43'E. 39°52’N), point В (121°2FE, 40°30’N), point C (117°57^{!}E, 38°39’N), point D (121°24’E, 40°38’N), point E (121°24’E, 40°38’N) and point F (119°25’E, 37°59’N) in the Bohai Sea and Yellow Sea were carried out, and the results are shown in Table 2.3 and Figures 2.28 through 2.40. It can be seen that the simulated tidal current is close to the actually observed tidal current and their velocity, direction, high and low tidal current and the turn of tidal current are basically the same.
The current observation data of Liaodong Bay in March 2009 were selected for comparison. The points compared were No.l (120°35.827’E, 40^{C}T8.619’N)
TABLE 2.3: Comparison between observed and simulated tidal current results in the Bohai Sea and Yellow Sea
Point 
Time 
Current velocity 
Current direction 

Relative error% 
Correlation coefficient 
Relative error% 
Correlation coefficient 

A 
1997.8.1617 
8.8 
0.97 
9.8 
0.90 
A 
1997.8.2324 
9.8 
0.90 
5.2 
0.98 
A 
1997.7.1516 
9.8 
0.95 
9.8 
0.91 
A 
1997.7.2526 
7.1 
0.96 
9.7 
0.95 
A 
1998.5.2223 
5.8 
0.99 
9.6 
0.94 
В 
1991.1.1920 
9.6 
0.90 
4.7 
0.97 
C 
1991.12.910 
9.8 
0.91 
10 
0.92 
C 
1991.12.1415 
9.9 
0.93 
7.1 
0.96 
D 
1988.10.2425 
8.3 
0.94 
9.3 
0.92 
E 
1989.9.34 
9.5 
0.91 
6.5 
0.97 
E 
1989.11.23 
9.3 
0.89 
9.7 
0.96 
E 
1988.7.1920 
6.6 
0.99 
9.3 
0.93 
F 
1988.8.34 
9.7 
0.88 
9.6 
0.87 
FIGURE 2.28: Comparison between observed and simulated tidal current on August 16 and 17, 1997, at point A (left: current velocity, the relative error is 8.8% and the correlation coefficient is 0.97; right: current direction, relative error is 9.8% and the correlation coefficient is 0.90)
FIGURE 2.29: Comparison between observed and simulated tidal current on August 23 and 24, 1997. at point A (left: current velocity, the relative error is 9.9% and the correlation coefficient is 0.90; right: current direction, relative error is 5.2% and the correlation coefficient is 0.98)
FIGURE 2.30: Comparison between observed and simulated tidal current on July 15 and 16, 1997, at point A (left: current velocity, the relative error is 9.8% and the correlation coefficient is 0.95; right: current direction, relative error is 9.8% and the correlation coefficient is 0.91)
FIGURE 2.31: Comparison between observed and simulated tidal current on J uly 25 and 26, 1997, at point A (left: current velocity, the relative error is 7.1% and the correlation coefficient is 0.96; right: current direction, relative error is 9.7% and the correlation coefficient is 0.95)
FIGURE 2.32: Comparison between observed and simulated tidal current on May 22 and 23, 1998, at point A (left: current velocity, the relative error is 5.8% and the correlation coefficient is 0.99; right: current direction, relative error is 9.6% and the correlation coefficient is 0.94)
FIGURE 2.33: Comparison between observed and simulated tidal current on January 19 and 20, 1991, at point В (left: current velocity, the relative error is 9.6% and the correlation coefficient is 0.90; right: current direction, relative error is 4.7% and the correlation coefficient is 0.97)
FIGURE 2.34: Comparison between observed and simulated tidal current on December 9 and 10, 1991, at point C (left: current velocity, the relative error is 9.8% and the correlation coefficient is 0.91; right: current direction, relative error is 10% and the correlation coefficient is 0.92)
FIGURE 2.35: Comparison between observed and simulated tidal current on December 14 and 15, 1991, at point C (left: current velocity, the relative error is 9.9% and the correlation coefficient is 0.93; right: current direction, relative error is 7.1% and the correlation coefficient is 0.96)
FIGURE 2.36: Comparison between observed and simulated tidal current on October 24 and 25, 1988, at point D (left: current velocity, the relative error is 8.3% and the correlation coefficient is 0.94; right: current direction, relative error is 9.3% and the correlation coefficient is 0.92)
FIGURE 2.37: Comparison between observed and simulated tidal current on September 3 and 4, 1989, at point E (left: current velocity, the relative error is 9.5% and the correlation coefficient is 0.91; right: current direction, relative error is 6.5% and the correlation coefficient is 0.98)
FIGURE 2.38: Comparison between observed and simulated tidal current on November 2 and 3. 1989, at point E (left: current velocity, the relative error is 9.3% and the correlation coefficient is 0.89; Right: current direction, relative error is 9.7% and the correlation coefficient is 0.96)
FIGURE 2.39: Comparison between observed and simulated tidal current on July 19 and 20, 1988, at point F (left: current velocity, the relative error is 6.6% and the correlation coefficient is 0.99; right: current direction, relative error is 9.3% and the correlation coefficient is 0.93)
FIGURE 2.40: Comparison between observed and simulated tidal current on August 3 and 4, 1988, at point F (left: current velocity, the relative error is 9.7% and the correlation coefficient is 0.88; right: current direction, relative error is 9.6% and the correlation coefficient is 0.87) and No.2 (120°38.35’E, 40°17.178’N). There are four comparison processes, as shown in Figures 2.41 through 2.44. respectively. The comparison indicates that the simulation results are in good agreement with the observed results.
The observed marine current at five points (i.e., Hi: 120°15.5’E, 34^{0}21.5’N; H2: 120°17.5’E, 34°24’N; H3: 120°17^{!}E, 34°19’N; H4: 120°21’E, 34°21’N; H5:
FIGURE 2.41: Comparison between observed and simulated tidal current on March 13 and 14. 2009, at point No.l (left: velocity; right: direction))
FIGURE 2.42: Comparison between observed and simulated tidal current on March 13 and 14, 2009, at point No.2 (left:velocity; right: direction)
FIGURE 2.43: Comparison between observed and simulated tidal current on March 9 and 10, 2009, at point No.l (left: velocity; right: direction)
120°20’E, 34°15’N) in the Yellow Sea area near Lianyungang on September 7 and 8, 2006, were selected for comparison. The results are shown in Figures 2.45 through 2.49. The current velocity and direction of the simulated tidal current are highly consistent with that, of the observed tidal current, indicating that the model results can basically describe the right tidal current process.
FIGURE 2.44: Comparison between observed and simulated tidal current on March 7 and 8, 2009, at point No.2 (left: velocity; right: direction)
FIGURE 2.45: Comparison between observed and simulated tidal current on September 7 and 8, 2006, at point Hi (left: velocity; right: direction)
FIGURE 2.46: Comparison between observed and simulated tidal current on September 7 and 8, 2006, at point H2 (left: velocity; right: direction)
FIGURE 2.47: Comparison between observed and simulated tidal current on September 7 and 8, 2006, at point H3 (left: velocity; right: direction)
FIGURE 2.48: Comparison between observed and simulated tidal current on September 7 and 8, 2006, at point H4 (left: velocity; right: direction)
FIGURE 2.49: Comparison between observed and simulated tidal current on September 7 and 8, 2006, at point H5 (left: velocity; right: direction)
The observed data at two points in Laizhou Bay (i.e., LI: 118°55.650’E, 38°11.600’N; L2: 118°53.553’E. 38°8.547^{:}N) on April 28 and 29, 2004, were selected for comparison and the results are shown in Figures 2.50 through 2.51 respectively. The comparison shows that the simulation results are consistent with the observation results and can represent the actual tidal current process.
FIGURE 2.50: Comparison between observed and simulated tidal current on April 28 and 29, 2004, at point Ll (left: velocity; right: direction)
FIGURE 2.51: Comparison between observed and simulated tidal current on April 28 and 29, 2004, at point L2 (upper: direction; lower: velocity)
(3) Sea level verification
A total of 12 comparisons of the data at point BHl (119°25'E, 37°59’N), point BH2 (117°57"E, 38°39'N), point BH3 (121°24'E, 40°38’N) and point BH4 (120°43’E, 39°52’N) were carried out. The results are as follows: 1) Point BHl (Figures 2.52 through 2.54): the relative error between the simulated value and the observed value is 5.4%, the root mean square error is 0.0333 and the correlation coefficient is 0.91. 2) Point BH2 (Figures 2.55 through 2.58): the relative error between the simulated value and the observed value is 5.1%, the root mean square error is 0.0301 and the correlation coefficient is 0.93.
FIGURE 2.52: Comparison of sea levels at point BHl on August 29 and 30, 1988
FIGURE 2.54: Comparison of sea levels at point BHl from August 2 to 5, 1988
FIGURE 2.56: Comparison of sea levels at point BH2 from December 25 to 28, 1991
00:00 02/12 00:00 03/12 00:00 04/12 00:00 05/12
FIGURE 2.58: Comparison of sea levels at point BH2 from December 2 to 5, 1991
FIGURE 2.60: Comparison of sea levels at point BH3 from October 22 to 29, 1988
FIGURE 2.62: Comparison of sea levels at point BH4 on October 13 and 14, 1997
FIGURE 2.63: Comparison of sea levels at point BH4 from May 21 to 23, 1998
3) Point ВИЗ (Figures 2.59 through 2.61): the relative error between the simulated value and the observed value is 10.1%, the root mean square error is 0.025 and the correlation coefficient is 0.90. 4) Point BH4 (Figures 2.62 through 2.63): the relative error between the simulated value and the observed value is 5.8%, the root mean square error is 0.013 and the correlation coefficient is 0.90. The comparison results indicate that the simulated sea level agrees well with the actually observed sea level, the root mean square error is basically within 0.1 cm, the ratio of the observed deviation to the mean value is less than 10% and the correlation coefficient is generally greater than 0.9.
Through the above comparison of harmonic constant, tidal current and sea level, it can be found that the FVCOM model can better simulate the characteristics of tide and tidal current in the Bohai Sea and Yellow Sea, and it can be affirmed that such a model can be reliably used to forecast the conditions of the Bohai Sea and Yellow Sea, and the forecast results truly reflect the current field characteristics of the forecasted sea areas.